# Complex variables conformal mapping trig identity

## Homework Statement

map the function $$$$w = \Big(\frac{z-1}{z+1}\Big)^{2}$$$$
on some domain which contains $$z=e^{i\theta}$$. $$\theta$$ between 0 and $$\pi$$
Hint: Map the semicircular arc bounding the top of the disc by putting $$z=e^{i\theta}$$ in the above formula. The resulting expression reduces to a simple trig function.

## Homework Equations

I can get the map if I can figure out what function they're going for, but I have no idea what function this is.

## The Attempt at a Solution

$$w = \Big(\frac{e^{i\theta}-1}{e^{i\theta}+1}\Big)^{2}$$
Where the heck do I go from here?

## Answers and Replies

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